Four-cluster chimera state in non-locally coupled phase oscillator systems with an external potential

Dynamics of a one-dimensional array of non-locally coupled Kuramoto phase oscillators with an external potential is studied. A four-cluster chimera state is observed for the moderate strength of the external potential. Different from the clustered chimera states studied before, the instantaneous frequencies of the oscillators in a synchronized cluster are different in the presence of the external potential. As the strength of the external potential increases, a bifurcation from the two-cluster chimera state to the four-cluster chimera states can be found. These phenomena are well predicted analytically with the help of the Ott–Antonsen ansatz.